All programs on the Librem5 appear to be in Debian packages and most of them seem to be identical to the ones in Debian. The document you cited has procedures for getting packages in PureOS independently of Debian, but it seems that most of it will be stock Debian. For my development it seems easier to just upload to Debian and wait for the next Debian release for it to be officially part of PureOS, I'll setup my own apt repository for the things I do and publish the URL for anyone who's interested.
As for apps being suspended, most apps are suspended when there's nothing to do. If a graphical application is minimised so it doesn't have to redraw the screen then it should either be doing nothing or occasionally polling a server if that's it's design.
Web browsers are an interesting corner case as web sites often have JavaScript that wants to run all the time and there's some trade-off between doing what the web site wants and saving CPU/energy. But that's probably not going to be an OS issue for PureOS but an Epiphany browser issue.